+1 for Mossberg 500/590-series models.
I'm a big fan of the Mossberg 590A1 for tactical use and/or HD. I'm a LEO, with 15 years in LE and 9+ years experience in Army SF and MI. My PD carries 14" Mossberg 590A1's for duty use in our cruisers. We used to carry the Remington 870's for duty, but for some reason we switched to the Mossbergs more than 10 years ago. I'm not sure why we did so.
I prefer the Mossberg 590A1 to the Remington 870, but that's just my own personal preference. The Mossberg 590A1 seems more sturdy and solid and its controls feel more intuitive to me.
However, if you are dead set on using a pistol grip on your shotgun, then the Remington 870, which is also an excellent shotgun, may be a better choice due to its safety location near the trigger. The Mossberg's tang safety is an awkward reach with a pistol grip. I prefer a rifle stock on my shotgun and the tang safety seems more intuitive. It gives you the ability to quickly view the weapon's condition while the shotgun is at the ready and on target without even impeding your cheek weld.
Also, it is my very strong opinion that a light source is MANDATORY for any HD weapon so as to be able to positively identify your potential target! Lest it be a family member, such as a teen son/daughter sneaking back into the house...that could be extremely tragic.
My personal favorite is my 14 inch barreled 12 gauge Mossberg 590A1 shotgun with ghost ring sights, a Hogue Youth stock, a Surefire 621FGA Forend Weaponlight, Blackhawk front sling adapter, Specter Gear 3-point tactical sling, and 3GunGear.com 7-Shell Side Saddle, which has a nylon side saddle with elasticized shell holders backed with velcro that affixes to a base on the shotgun receiver. This side saddle carrier allows single-hand removal and attachment so that additional side saddle carriers can be carried on tactical vests or plate carriers and your ammo source can be easily and quickly replenished. This shotgun has an overall length (OAL) of 35 inches, which is a nice compact size for manuevering inside a house or building. This is my primary HD long gun.
As far as optics, I've never used anything other than a bead sight or ghost rings on my work or personal shotguns. The 590A1 comes with very good factory ghost ring sights. I would try using the ghost rings for a while before getting some additional optic, such as a red dot or low power scope. The ghost ring sight with a tritium or fiber optic front blade may be sufficient, since the shotgun is primarily a close quarters weapon.
As far as ammo, one of the best things about a shotgun is its versatility, to include an abundance of ammo selection for different situations. For the most part, a pump shotgun will be able to use a greater variety of ammo and have less feed problems than a semi-auto shotgun. What you lose with a pump is speed on follow-up shots, but with training one can minimize this.
I know from personal use that my Mossberg 590A1 eats everything I've ever fed her! She's my work horse and one nasty beast!